Experimental and Numerical Study of Evolution of Statistical Properties of Unidirectional Narrow-Banded Steep Wave Groups

Unidirectional random waves generated by a wavemaker in a 300-mlong wave tank are investigated experimentally. Spatial evolution of numerous statistical wave field parameters is studied. It is found that the frequency spectrum of the wave field undergoes significant variation in the course of its evolution along the tank; the values of all statistical wave parameters are strongly related to the local spectral width. The deviations of various statistical parameters from the Gaussian statistics increase with the width of the spectrum, so that the probability of extremely large (the so-called freak) waves is highest when the local spectral width attains maximum. It is found that the third-order random wave field model of Tayfun and Fedele [1] provides an appropriate description of the observed phenomena. The laboratory runs are reproduced through numerical simulations of the spatial form of the Dysthe equation. The simulation reproduce the wave shapes observed in laboratory, though for very steep waves some deviations in the computed wave shapes and the envelopes from those measured in the tank were observed at larger distances.